Gluonic fields of a static particle to all orders in 1/N

We determine the expectation value of the gauge invariant operator Tr [F^2+... ] for N=4 SU(N) SYM, in the presence of an infinitely heavy static particle in the symmetric representation of SU(N). We carry out the computation in the context of the AdS/CFT correspondence, by considering the perturbation of the dilaton field caused by the presence of a D3 brane dual to such an external probe. We find that the effective chromo-electric charge of the probe has exactly the same expression as the one recently found in the computation of energy loss by radiation.